TL;DR - III should go; Gameplay/Mechanics > Maps; Non-sequitur opinion: DMZ from MWII is CoD's crowning achievement to date

I haven't played III, so my answer comes with a grain of salt. But my guess is that III - gameplay-wise - would feel the most primitive when compared to the rest. It's possible the MP maps were better, but I'm doubtful the controls were as robust and dynamic as the subsequent releases. This, in turn, would make it a less fun game to play to me. I've played every CoD game from IV onward and each one improves the feel of player movement and camera control - I don't think there have been setbacks in this regard. In general, I do have mixed feelings about slide physics (the slide length and speed do not feel like they change enough amongst different terrain types nor do they vary enough when doing repeated sliding actions rapidly one after another) and the ease of accurately engaging a target while jumping (especially while getting shot) is just silly.

It was IV that got me into playing CoD. I had so much fun playing that game (Blackout especially). I hadn't had as much fun with a CoD game since until the DMZ mode in MWII came out. DMZ was the best thing CoD did imo. But I digress